Pseudogap formation and quantum phase transition in strongly-correlated electron systems

Pseudogap formation is a ubiquitous phenomenon in strongly-correlated superconductors, for example cuprates, heavy-fermion superconductors, and iron pnictides. As the system is cooled, an energy gap opens in the excitation spectrum before entering the superconducting phase. The origin of formation and the relevancy to the superconductivity remain unclear, which is the most challenging problem in condensed matter physics. Here, using the cuprate as a model, we demonstrate that the formation of pseudogap is due to a massive gauge interaction between electrons, where the mass of the gauge boson, determining the interaction length scale, is the consequence of the remnant antiferromagnetic fluctuation inherited from the parent compounds. Extracting from experimental data, we predict that there is a quantum phase transition belonging to the 2D XY universality class at the critical doping where pseudogap transition vanishes.